That's already happened in the US.[1] The Buffalo Commons proposal, to depopulate a large part of the Great Plains and let buffalo roam, was a joke when it was first proposed in 1987. Much of the depopulation has already happened. So far, not many buffalo, but they may come back.
Small town America is slowly emptying out.[2] It has no function. Small towns existed mostly to support agriculture. Agriculture is only 3% of the US workforce. Most of the food comes from about 20% of the farms; the rest are marginal producers. Farming is doing fine; it just doesn't take many people.
"Mill towns", where one big employer dominates, die when their mill closes. These can be sizable cities, such as Youngstown, OH. More often, they're small towns with one big plant. Young people leave; old people stay and die in place.
[1] https://en.wikipedia.org/wiki/Buffalo_Commons [2] http://www.wsj.com/articles/SB100014240527023033252045794637...